For the purpose of driving a supercharger, use of a continuously variable transmission is known. Japanese Laid-Open Utility Model No. 61-32525 shows a supercharging system in which a supercharger is driven mechanically by an output shaft of an engine through a continuously variable transmission wherein the gear ratio of the continuously variable transmission is controlled precisely to obtain an optimum rotational speed of supercharger in accordance with engine operating conditions. Use of a continuously variable transmission, however, requires variable pulleys and accompanying complex mechanisms too large to install in a narrow engine space or, room. The diameters of the pulleys are normally designed to be relatively large in order to change gear ratio effectively over a wide range. Furthermore, actuators required for driving the pulleys are disposed beside the pulleys.